United produced their best performance of the season as Louis van Gaal's fourth-placed side easily accounted for Tottenham 3-0 at Old Trafford, to move within two points of City, who were stunned 1-0 by lowly Burnley.
A top-four finish is the top priority for United but Smalling sees no reason as to why the Manchester club cannot pip City to second.
"I think we could [finish second], especially after City's result on Saturday," he said. "It is all very close.
"There is only a point between us and Arsenal. I think it's very open all the way up to second place and we will be aiming for that, especially when we are playing those teams coming up.
"We want Champions League football back here. It's a must. Fourth is the minimum but when it's there, second is a realistic target and if we keep on performing like that I don't see why we can't give it a good push."
If United are to secure UEFA Champions League football next season, let alone finish second, they must get a result at Liverpool on Sunday.
"We knew how big the game on Sunday was. You talk about six-pointers ... these games coming up are all pretty much six-pointers where we can do ourselves a favour and do our rivals big damage as well. Spurs was the first step," the Englishman added.
"It was the perfect time to put in a performance like that, especially with our run of fixtures.
"I think we can do ourselves a lot of favours but then I think we can obviously with the teams around us, these are like six-point games so we have got a lot to play for. We can do ourselves a lot of good."
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